A device for obtaining a conoscopic holograph using incoherent light is described in patent document U.S. Pat. No. 4,602,844.
The device described in that document includes, as illustrated diagrammatically in accompanying FIG. 1, a birefringent crystal inserted between two circular polarizers.
The crystal decomposes an incident ray firstly into an ordinary ray subjected to a refractive index n.sub.o, and secondly into an extraordinary ray subjected to a refractive index which varies as a function of the angle of incidence .theta., with this variable refractive index being written n.sub.e (.theta.).
These two rays propagate at different speeds within the crystal. As a result they are at different phases on leaving the crystal. Conographic holography is based on the fact that this phase difference is a function of the angle of incidence .theta.. The two rays interfere after passing through the outlet polarizer such that the intensity of the resulting ray is also a function of the angle .theta.. In other words, unlike conventional holography, each incident ray produces its own reference ray. The set of rays situated on a cone whose axis is parallel to the optical axis of the crystal and having an aperture angle .theta. will give the same intensity on the observation plane.
The conoscopic hologram of a point obtained by means of the above-mentioned device corresponds to a Fresnel zone as shown in accompanying FIG. 2, i.e. a series of concentric annular interference fringes.
The conoscopic hologram of an object is the superposition of the holograms of each of the points constituting the object. FIGS. 3b and 3c of above-mentioned patent document U.S. Pat. No. 4,602,844 respectively show the holograms for two points and for three points of a plane object.
The resulting hologram contains all of the useful information, such that it is possible to reconstruct the initial object in three dimensions.
The conoscopic system performs a linear transformation between the object and its hologram.
The impulse response of the system, which characterizes the linear transformation, is written: EQU T(x',y')=1+cos(.alpha.r.sup.2) (1)
where r.sup.2 =x'.sup.2 +y'.sup.2, and:
.alpha.=2.pi.L.delta.n/.lambda.n.sub.o.sup.2 Z.sub.c.sup.2 ( 2)
with
.lambda.=source wavelength
L=crystal length
n.sub.o =the ordinary index of the crystal
.delta.n=the absolute value of the difference between the ordinary and extraordinary indices
x,y,z=coordinates in the object volume
x',y'=coordinates in the hologram plane EQU Z.sub.c =Z(x,y)-L+L/n.sub.o ( 3)
where Z(x,y) is the distance between the holographic plane and the object point under consideration, situated at the lateral position (x,y). The Fresnel parameter .alpha. can also be written: EQU .alpha.=.pi./ .sub.eq (Z.sub.c)Z.sub.c ( 4)
thus defining an equivalent wavelength .lambda..sub.eq : EQU .lambda..sub.eq =.lambda.n.sub.o.sup.2 Zc/.delta.n2L (5)
or: EQU .alpha.=.pi./.lambda.f.sub.c ( 6)
thus defining the focal length f.sub.c of the Fresnel lens: EQU f.sub.c =n.sub.o.sup.2 Z.sub.c.sup.2 /.delta.n2L (7)
When the object under consideration is plane (.alpha.=constant) the equivalent wavelength and the focal length f.sub.c are constants of the system.
Equation (4) then shows that the conoscopic hologram of a point recorded at a wavelength .lambda. is similar to the hologram of the same point recorded using coherent light (Gabor holography) at the equivalent wavelength .lambda..sub.eq. It should be observed that the conoscopic hologram measures intensities and not amplitudes.
Since the distances Z.sub.c and L are of the same order and since .delta.n is about 0.1, the wavelength .lambda..sub.eq is greater than the real wavelength .lambda. at which recording takes place: typically .lambda..sub.eq =3 .mu.m to 100 .mu.m.
As a result, the lateral resolution in the hologram (proportional to the wavelength .lambda.) is less in conoscopic holography than in conventional holography. Its value lies around a few tens of micrometers.
As mentioned above, the hologram recorded using a conoscopic device contains all of the useful information.
For example, for the hologram of a point corresponding to a Fresnel zone:
the center of the zone and the object point lie on the same straight line parallel to the optical axis, and if the object point is translated transversely or laterally, then the hologram is translated identically in the holographic plane; the coordinates of the center C(x.sub.o, y.sub.o) of the Fresnel zone are thus equal to the first two coordinates of the holographed point P(x.sub.o, y.sub.o, z.sub.o);
the intensity of the hologram gives the light energy in the light aperture cone; and
the spacing of the fringes gives the distance between the object and the observation plane, independently of the position of the conoscopic device.
The following may be written: EQU Z.sub.c =R.sup.2 /F.lambda..sub.eq ( 8)
and EQU Z(x,y)=Z.sub.c +L-L/n.sub.o =R.sup.2 /F.lambda.eq+L-L/n.sub.o( 9)
where R is the radius of the Fresnel zone, and F is the number of light and dark fringes on the radius.
In spite of the great hopes based on conscopic holography as described above, it has not yet lead to industrial developments.
This appears to be due to the fact that it is relatively difficult to make use of a hologram obtained in this way.
The inventors have observed that the conoscopic hologram also contains two types of interfering information, corresponding respectively to a coherent continuous background or "bias", and to a conjugate image, both of which degrade the basic information which is sufficient on its own for reconstructing the object.
These two types of interfering information which are superposed on the useful information when a conoscopic hologram is recorded can be shown up by illuminating the conoscopic hologram recorded on a photosensitive film by means of a monochromatic plane wave. Three diffractive beams are then observed: the first beam represents the wave transmitted directly through the film and corresponds to the bias; the second wave is a spherical wave diverging from a virtual object which is a replica of the original object; and the third wave is a spherical wave converging on a conjugate real image of the object situated symmetrically to the virtual image about the plane of the hologram.
The two above-mentioned interfering types of information (bias and conjugate image) can also be shown up by the following, more theoretical approach.
For plane objects, the linear transformation between the intensity I(x,y) of the object and the intensity H(x',y') of the hologram is given by the convolution: EQU H(x',y')=I(x,y)*T(x,y) (10)
After the convolution equation (10) has been developed, the hologram appears as a Fresnel transform: EQU H(x',y')=I.sub.o +I(x,t)*cos(.alpha.r.sup.2) (11)
or EQU H(x',y')=I.sub.o +1/2I(x,t)*e.sup.-j.alpha.r.spsp.2 ( 11)
where I.sub.o represents the bias intensity which penetrates directly through the system, and 1/2I(x,y)*e.sup.-jar.sup.2 represents the conjugate image.
The object of the present invention is to propose means for eliminating the bias and the conjugate image from the recorded hologram.